1. Field of the Invention
The present invention relates generally to a method of seismic data modeling and the interpretation and estimating of earth parameters from seismic data. More particularly, the present invention relates to a method of incorporating and accounting for the effects of anisotropy in seismic applications.
2. Description of the Related Art
Seismic data acquisition involves the generation of seismic waves in the earth using an appropriate source or sources and the recording of the response of the earth to the source waves. Seismic data is routinely acquired to obtain information about subsurface structure, stratigraphy, lithology and fluids contained in the earth's rocks. The seismic response is in part generated by the reflection of seismic waves in the subsurface where there are changes in those earth properties that impact seismic wave propagation. The process that describes how source signals propagate and how the response is formed is termed seismic wave propagation.
Modeling is used to gain understanding of seismic wave propagation and to help analyze seismic signals. In modeling, a model of earth properties is posed and a seismic wave propagation modeling algorithm is used to synthesize seismic responses. For purposes of the present invention, modeling is assumed to include the synthesis of the amplitudes of reflected seismic waves. Models of earth properties are often specified in terms of physical parameters. An example is the group of modeling methods that today are widely used to study changes in seismic reflection amplitudes with changing angle of incidence of a plane wave reflecting from a flat interface. See Castagna, J. P. and Backus, M. M., “Offset-dependent reflectivity—theory and practice of AVO analysis”, 1993, Investigations in Geophysics vol. 8, Society of Exploration Geophysicists, chapter I. In this model, the two half-spaces above and below the interface are assumed to be homogeneous and isotropic so that each half-space can be described with just three earth parameters, for example p-wave velocity, s-wave velocity and density. In practice alternative triplets of parameters may be used, for example p-wave impedance, s-wave impedance and density. These parameters are referred to as elastic parameters. In some cases, modeling methods start from other earth parameters, and the transforms to elastic parameters are included as part of the modeling method.
Many alternative modeling methods are described in the literature to tackle more complex models. One well-known extension to the above single interface model is to a stack of horizontal layers rather than just two and with incorporation of waves generated from a point source instead of plane waves. Another example involves the use of elastic impedance, as described by Connolly, P., 1999, “Elastic impedance”, The Leading Edge, April 1999, pp. 438-452. For more general cases a wide range of computational algorithms is available, often based on the use of finite difference schemes, as for example discussed by Mufti, I. R., and Fernandes, R. A. R., 1998, “A wave-equation splitting algorithm for seismic modeling with applications to anisotropic seismic media”, Society of Exploration Geophysicists 68th Annual Meeting Expanded Abstracts.
In seismic modeling methods seismic responses are synthesized given the earth parameters. Often this involves expressing changes in the elastic parameters across interfaces in terms of their relative contrasts. In the following, the term elastic parameter is deemed to also include relative elastic parameter contrasts. Seismic modeling is often referred to as forward modeling. The reverse process of forward modeling is called inverse modeling or inversion. The goal of inversion is to estimate earth parameters given the measured seismic responses. Many inversion methods are available. They all have in common that they are based on some forward model of seismic wave propagation. Buland, A., and Omre, H., 2003, “Bayesian Seismic Inversion and Estimation in a Spatial Setting”, European Association of Geoscientists and Engineers 65th Annual Conference Expanded Abstracts; Buland, A., and Omre, H., 2003, “Bayesian linearized AVO inversion”, Geophysics, volume 68, pp. 185-198; Fatti, J. L., Smith, G. C., Vail, P. J., Strauss, P. J., and Levitt, P. R., 1994, “Detection of gas in sandstone reservoirs using AVO analysis: A 3D seismic case history using the Geostack technique”, Geophysics, volume 59, pp. 1362-1376; Goodway, B., Chen, T., and Downton J., 1998, “Improved AVO fluid detection and lithology discrimination using Lamé´ petrophysical parameters; “λρ”, “μρ”, & “λ/μ fluid stack’, from P and S inversions”, Canadian Society of Exploration Geophysicists 1998 Annual Meeting Expanded Abstracts; Rasmussen, K. B., Veggeland, T., Espersen, T. B., Pedersen, J. M., and Maver, K. G., 2000, “Rock Properties Prediction Through AVO Seismic Inversion”, NPF Geophysical Biennial Geophysical Seminar Expanded Abstracts; Rutledal, H., Elde, R., Van Wijngaarden, A-J., Helgesen, J., Buran, H., and Weisser, T., 2002, “Time-lapse elastic inversion at the Oseberg field”, European Association of Geoscientists and Engineers 64th Annual Conference Expanded Abstracts; Smith, G. C., and Gidlow, P. M., 1987, “Weighted stacking for rock property estimation and detection of gas”, Geophysical Prospecting, volume 35, pp. 993-1014; Tonellot, T., Mace, D., and Richard, V., 2002, “3D quantitative AVA: Joint versus sequential stratigraphic inversion of angle-limited stacks”, Society of Exploration Geophysicists 72nd Annual Meeting Expanded Abstracts; Whitcombe, D. N., Connolly, P. A., Reagan, R. I., and Redshaw, T. C., 2000, “Extended elastic impedance for fluid and lithology prediction”, Society of Exploration Geophysicists 70th Annual Meeting Expanded Abstracts; and U.S. patent application Ser. No. 09/817,807 present examples of inversion methods that use the amplitudes of seismic data to estimate subsurface elastic parameters. Some of these methods make use of certain input elastic parameter data, for example in the form of low frequency trend information or statistical distributions. Other inversion methods do not use elastic parameters upon input, and use some calibration of seismic amplitudes, performed in a pre-processing step or as part of the algorithm. Alternatively, amplitude calibration is done in a post-processing step. Mostly inversion methods operate on an output elastic parameter data. However, some methods may work with other earth parameter data, where the transforms to elastic parameter data are incorporated into the method. Dependent on the seismic data acquisition geometries, estimates of earth rock properties obtained from any of these inversion methods are generally provided as a series of 2D sections or 3D volumes of elastic parameters.
An important component of modeling and inversion is the seismic wavelet. Many methods are available for wavelet estimation. It is generally advantageous to use available bore hole data or modeling results based on bore hole data in estimating wavelets, see e.g., Walden, A. T., and White, R. E., 1984, “On errors of fit and accuracy in matching synthetic seismograms and seismic traces”, Geophysical Prospecting, volume 32, pp. 871-891; and White, R., and Simm, R., Oct. 2003, “tutorial: Good practice in well ties”, First Break, volume 21, pp. 75-83. Alternatively, the amplitude and phase characteristics of wavelets initially obtained without making use of bore hole data are often refined or calibrated by making use of bore hole data or modeling results based on bore hole data.
Inversion is generally followed by a step of analysis and interpretation of the inversion results. Available bore hole log measurements are used to support the analysis and interpretation. To facilitate the comparison, it is desirable that the bore hole log data and the inversion results are matched. This may require transforms of the bore hole log data to the elastic parameters output with the inversion. Alternatively, the inversion results are transformed. When bore hole data and inversion results are available that are properly matched, interpretation can be highly automated, see for example U.S. patent application Ser. No. 09/579,695; and Bertrand, C., Tonellot, T., and Fournier, F., 2002, “Seismic facies analysis applied to P and S impedances from pre-stack inversion”, Society of Exploration Geophysicists 72nd Annual Meeting Expanded Abstracts. When bore hole data is not available, data from other bore holes that have comparable characteristics, model data or hypothetical data may be used. Also in these cases transforms may be advantageous to support matching between these data and the inversion results.
Conventional interpretation is done on the seismic data. To help understand the amplitude characteristics of the seismic data, seismic modeling is often performed using available bore hole data or data from analogues or hypothetical data. One example of incorporating seismic amplitude modeling results in seismic interpretation is described by Brown, A. R., 1996, “Interpretation of three-dimensional seismic data”, AAPG Memoir 42, American Association of Petroleum Geologists, chapter 6. Further, bore hole or model elastic parameter data is routinely visualized in conjunction with seismic data in support of the interpretation process.
Seismic data is bandlimited in nature. Therefore, in many modeling algorithms bandlimited seismic data can be conveniently synthesized by using de-trended or bandlimited earth elastic parameters in the input earth model or earth parameters from which the elastic parameters are derived as part of the modeling method. As already noted above, reference to earth parameters or elastic parameters is deemed to encompass relative contrasts in any such parameters also. Like modeling, inversion can be used to obtain bandlimited output earth parameters, as for example presented in Lancaster, S., and Whitcombe, D. N., 2000, “Fast-track ‘coloured’ inversion”, Society of Exploration Geophysicists 70th Annual Meeting Expanded Abstracts, and the analysis and interpretation step can be executed on bandlimited inversion results. Yet another alternative is provided by methods that output results in which the high frequency information (relative to the seismic bandwidth) is removed or suppressed. It is expressly noted that reference to any earth parameter includes bandlimited or de-trended earth parameters or earth parameters in which the high frequency information is removed or suppressed. It is further noted that reference to modeling, inversion, wavelet estimation and result analysis and interpretation methods encompasses methods that work on or output any such earth parameter data.
Most of today's routinely applied methods for forward modeling, wavelet estimation, inversion, analysis and interpretation of inversion results, and analysis and interpretation of seismic data have as a core assumption that the earth can be locally modeled by a stack of layers, wherein each layer is isotropic. Such methods are further referred to as “isotropic” methods. In actual fact, the earth subsurface is generally anisotropic and seismic data contains the effects of anisotropy. To distinguish such seismic data, it is termed anisotropic seismic data. The earth parameters that describe anisotropy are referred to as anisotropy parameters. To improve the accuracy of seismic modeling, wavelet estimation, inversion, and the analysis and interpretation of inversion results and seismic data in case of anisotropic seismic data requires that anisotropy is accounted for. Examples of methods to handle anisotropy are described by Rueger, A., 2002, “Reflection Coefficients and Azimuthal AVO Analysis in Anisotropic Media”, geophysical monograph series No. 10, Society of Exploration Geophysicists; and Thomsen, L., 2002, “Understanding Seismic Anisotropy in Exploration and Exploitation”, Distinguished Instructor Series No. 5, Society of Exploration Geophysicists/European Association of Geoscientists and Engineers.
Incorporation of the anisotropy parameters in these methods makes them mathematically and numerically more complex than the equivalent isotropic methods. Also methods where seismic modeling is used, such as in wavelet estimation and in certain seismic data analysis and interpretation methods, would need to be extended to incorporate the anisotropy parameters, making them more complex in utilization. Further, from the perspective of inversion, explicit incorporation of anisotropy parameters is even more disadvantageous. Already inversion for the elastic parameters from AVO seismic data is recognized to be a difficult problem for most seismic data acquisition geometries. Including the anisotropy parameters in inversion as parameters that also need to be recovered in the inversion process further increases the number of unknowns and makes the inverse problem more difficult. Addition of more parameters and coping with the difficulty also complicates the analysis and interpretation of inversion results.
Thus a need exists for a method of incorporating and generating anisotropy parameters in applications such as seismic modeling, wavelet estimation, inversion and the like, as well as analysis and interpretations of such data.